Simplify Square Root of 38009

What is the square root of 38009 in its simplest radical form? To be more specific, we have created an illustration below showing what we want to calculate. Our goal is to make "A" outside the radical (√) as large as possible, and "B" inside the radical (√) as small as possible.

√38009 = A√B

Unfortunately, the square root of 38009 cannot be simplified. Thus, here is the answer to the square root of 38009 in its simplest form:

√ 38009 = √ 38009

Here are two different methods we used to determine why the square root of 38009 cannot be simplified.

1) To be able to simplify the square root of 38009, one of the factors of 38009 other than 1 must be a perfect square. The factors of 38009 are 1, 191, 199, and 38009. Since none of these factors are perfect squares, the square root of 38009 cannot be simplified.

2) To be able to simplify the square root of 38009, all the prime factors of 38009 cannot be unique. When we did prime factorization of 38009, we found that 191 x 199 equals 38009. Since all the prime factors are unique, the square root of 38009 cannot be simplified.

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